Google says the Nexus 7, its hotly anticipated new tablet computer, is shipping to customers who preordered it this week, amid reports of heavy demand.

In an e-mail to customers, the company said some versions of the 7-inch tablet are in the mail and others would be on the way to customers by Thursday evening.

"We've had incredible demand for the new tablet and are shipping them as quickly as possible," read the message. "If you placed your order by July 11, it will ship this week, and we've upgraded to overnight shipping so it arrives sooner. Orders placed after July 11 will ship next week with overnight shipping."

At its online Help Center, Google says 8 GB versions of the Nexus 7 have already been shipped in the United States. All 16 GB versions that were ordered before July 11 should be shipped by the end of the day Thursday.

Orders in the UK and Australia will be shipped later this month.

Retailers have been reporting that they've already sold out of all of the Nexus 7s they've ordered.

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CNET reported this week that GameStop, Staples, Sam's Club and Office Depot already had sold out of the tablet. GameStop told the blog they expected another shipment on August 7.

A quick check of several websites Thursday, including Fry's and Best Buy, didn't turn up any that say they have the Nexus 7 in stock.

There have been scattered reports online of people who say they've already received a Nexus 7 or found one in stores. But, in an unusual move, Google has not announced an official date they'll go on sale in retail stores.

While all signs point to big sales, Google also remains mum on how many tablets have been ordered or shipped to retailers. In the past, some electronics companies have been suspected of intentionally limiting the supply of new products to create the appearance of strong demand.

Last month, Google announced it would be releasing its own, 7-inch tablet. It's a move that comes in the wake of the relative success Amazon has had with its smaller, less expensive iPad competitor, the Kindle Fire.

Analysts say the Kindle Fire sold roughly 16 million of the devices last year. That's as good as any tablet has done other than the Apple's iPad. Apple is expected to sell 55 million by the end of this year. The arrival of the Nexus 7 and a possible smaller iPad, however, have many wondering whether it will keep its momentum.

Like the Fire, which also has a 7-inch screen, the 8 GB Nexus 7 will sell for $199. A 16 GB version sells for $249.

"The Nexus 7, the first tablet to wear Google's Nexus brand, sets a new standard for smaller slates, proving that just because it isn't as big as Apple's iPad doesn't mean it can't be just as useful, as fast, or as fun," Nathan Olivarez-Giles wrote for Wired, a CNN content partner.